Questions: A gear has been designed to have a diameter of 4 inches. The standard deviation of the process is 0.3 inch. A control chart is shown. Each chart has horizontal lines drawn at the mean, μ, μ ± 2 σ, and at μ ± 3 σ. Determine if the process shown is in control or out of control. Explain. Is the process in control or out of control? Select all that apply. A. In control, because none of the three warning signals detected a change. B. Out of control, because a point lies more than three standard deviations beyond the mean. C. Out of control, because there are nine consecutive points either above or below the mean. D. Out of control, because two out of three consecutive points lie more than two standard deviations from the mean.

A gear has been designed to have a diameter of 4 inches. The standard deviation of the process is 0.3 inch. A control chart is shown. Each chart has horizontal lines drawn at the mean, μ, μ ± 2 σ, and at μ ± 3 σ. Determine if the process shown is in control or out of control. Explain.

Is the process in control or out of control? Select all that apply.
A. In control, because none of the three warning signals detected a change.
B. Out of control, because a point lies more than three standard deviations beyond the mean.
C. Out of control, because there are nine consecutive points either above or below the mean.
D. Out of control, because two out of three consecutive points lie more than two standard deviations from the mean.

Transcript text: A gear has been designed to have a diameter of 4 inches. The standard deviation of the process is 0.3 inch. A control chart is shown. Each chart has horizontal lines drawn at the mean, $\mu, \mu \pm 2 \sigma$, and at $\mu \pm 3 \sigma$. Determine if the process shown is in control or out of control. Explain. Is the process in control or out of control? Select all that apply. A. In control, because none of the three warning signals detected a change. B. Out of control, because a point lies more than three standard deviations beyond the mean. C. Out of control, because there are nine consecutive points either above or below the mean. D. Out of control, because two out of three consecutive points lie more than two standard deviations from the mean.

Solution

Solution Steps

Step 1: Analyze the control chart

The control chart shows the diameter measurements of the gears. The mean diameter is 4 inches, and the standard deviation is 0.3 inches. The chart has lines drawn at the mean, μ ± 2σ, and μ ± 3σ. Visually, we can see all points are within μ ± 3σ, ruling out option B. There are not nine consecutive points above or below the mean (μ). The points fluctuate above and below the mean throughout the chart, eliminating option C.

Step 2: Investigate control signals

No points lie outside the μ ± 3σ control limits. We need to consider the warning signals to determine if the process is out of control. The given options mention some of these warning signals, so let's examine them:

Two out of three consecutive points lie beyond μ ± 2σ: This does not occur on the chart.
Four out of five consecutive points lie beyond μ ± σ: This does not occur on the chart.
Nine consecutive points lie on one side of the mean: This does not occur on the chart.

Step 3: Determine if the process is in control

Since none of the warning signals are present, and all points lie within the control limits, the process is considered in control.